Most of the course focuses on using numerical methods to approximate solutions to problems that cannot be solved analytically. Because these methods can be tedious, the computational power we have these days makes implementing the methods drastically easier. Therefore, the learning objectives for the course include understanding the mathematical basis for numerical methods across an array of problem types and implementing these methods computationally in Python.

Module 1

• Introduction to Computational Thinking
• Introduction to AI (ChatGPT)
• Python Coding Bootcamp Lecture

Module 2: Approximations and Errors

• Binary Numbers: Round-off Errors
• Taylor Series: Truncation Errors

Module 3: Numerical Differentiation and Integration

• Divided Difference Approximations
• Numerical Integration

Module 4: Linear Algebra

• Vectors and Matrices
• Linear Systems: Gaussian Elimination
• Interpolation
  • Polynomial interpolation
  • B-spline interpolation

Module 5: Optimization

• Single variable optimization
  • Golden Section Search
  • Newton’s Method
  • Steepest Ascent
• Multivariable optimization
  • Gradients and Hessians
  • Gradient Methods

Module 6: Regression

• Linear regression
• Nonlinear regression

Module 7: ODEs

• ODE Introduction and Nomenclature; Euler’s Method Lecture
• Midpoint Method
• Runge-Kutta 4th Order Method

Module 8: Machine Learning

• Introduction to machine learning
  • Bias/variance tradeoff
  • Regression as a ML model
• Supervised vs unsupervised methods
  • Clustering
  • Classification
• Introduction to deep learning methods

Module 9: MATLAB Bootcamp